On structural properties of generalized Cayley graphs

Abstract

In this paper, firstly, we provide some necessary and sufficient conditions for generalized Cayley graphs of finite abelian groups to be bipartite. Secondly, we deduce several necessary and sufficient conditions for generalized Cayley graphs of finite groups to be connected. At last, as a by-product, we determine the groups whose all cubic generalized Cayley graphs are connected and integral.